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In this contribution we propose an optimally stable ultraweak Petrov-Galerkinvariational formulation and subsequent discretization for stationary reactivetransport problems. The discretization is exclusively based on the choice ofdiscrete approximate test spaces, while the trial space is a priori infinitedimensional. The solution in the trial space or even only functionalevaluations of the solution are obtained in a post-processing step. We detailthe theoretical framework and demonstrate its usage in a numerical experimentthat is motivated from modeling of catalytic filters.

An optimally stable approximation of reactive transport using discrete test and infinite trial spaces